{"id":79,"date":"2023-08-05T16:44:39","date_gmt":"2023-08-05T16:44:39","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e6%95%b0%e5%ad%a6%e7%9a%84%e3%81%aa%e6%9c%9f%e5%be%85%e5%80%a4%e3%81%be%e3%81%9f%e3%81%af%e6%9c%9f%e5%be%85%e5%80%a4\/"},"modified":"2023-08-05T16:44:39","modified_gmt":"2023-08-05T16:44:39","slug":"%e6%95%b0%e5%ad%a6%e7%9a%84%e3%81%aa%e6%9c%9f%e5%be%85%e5%80%a4%e3%81%be%e3%81%9f%e3%81%af%e6%9c%9f%e5%be%85%e5%80%a4","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e6%95%b0%e5%ad%a6%e7%9a%84%e3%81%aa%e6%9c%9f%e5%be%85%e5%80%a4%e3%81%be%e3%81%9f%e3%81%af%e6%9c%9f%e5%be%85%e5%80%a4\/","title":{"rendered":"\u6570\u5b66\u7684\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024)"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024) \u3068\u306f\u4f55\u304b\u3001\u304a\u3088\u3073\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u6570\u5b66\u7684\u5e0c\u671b\u306e\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\u304c\u898b\u3064\u304b\u308b\u3067\u3057\u3087\u3046\u3002\u3055\u3089\u306b\u3001\u30aa\u30f3\u30e9\u30a4\u30f3\u8a08\u7b97\u6a5f\u3092\u4f7f\u7528\u3057\u3066\u3001\u4efb\u610f\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u671f\u5f85\u5024\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\" id=\"que-es-la-esperanza-matematica-o-valor-esperado\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-esperanza-matematica-o-valor-esperado\"><\/span>\u6570\u5b66\u7684\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024) \u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7d71\u8a08\u5b66\u3067\u306f\u3001<strong>\u671f\u5f85<\/strong>\u5024 (<strong>\u671f\u5f85\u5024<\/strong>\u3068\u3082\u547c\u3070\u308c\u307e\u3059) \u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u5e73\u5747\u5024\u3092\u8868\u3059\u6570\u5024\u3067\u3059\u3002\u6570\u5b66\u7684\u306a\u671f\u5f85\u5024\u306f\u3001\u30e9\u30f3\u30c0\u30e0\u306a\u30a4\u30d9\u30f3\u30c8\u306e\u5024\u3068\u305d\u308c\u305e\u308c\u306e\u767a\u751f\u78ba\u7387\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u3059\u3079\u3066\u306e\u7a4d\u306e\u5408\u8a08\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u671f\u5f85\u5024\u306e\u8a18\u53f7\u306f\u5927\u6587\u5b57\u306e E \u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u7d71\u8a08\u5909\u6570 X \u306e\u671f\u5f85\u5024\u306f E(X) \u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u540c\u69d8\u306b\u3001\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024\u306f\u305d\u306e\u5e73\u5747\u5024 (\u6bcd\u96c6\u56e3\u5e73\u5747) \u3068\u4e00\u81f4\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\" id=\"como-calcular-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"como-calcular-la-esperanza-matematica\"><\/span>\u6570\u5b66\u7684\u671f\u5f85\u5024\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u96e2\u6563\u5909\u6570\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u624b\u9806\u306b\u5f93\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u8003\u3048\u3089\u308c\u308b\u5404\u30a4\u30d9\u30f3\u30c8\u306b\u305d\u306e\u767a\u751f\u78ba\u7387\u3092\u639b\u3051\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:12px\"><span style=\"color:#101010;font-weight: normal;\">\u524d\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u5f97\u3089\u308c\u305f\u3059\u3079\u3066\u306e\u7d50\u679c\u3092\u5408\u8a08\u3057\u307e\u3059\u3002<\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\u53d6\u5f97\u3055\u308c\u305f\u5024\u306f\u3001\u5909\u6570\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024) \u3067\u3059\u3002<\/span><\/li>\n<\/ol>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u96e2\u6563\u5909\u6570\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024) \u3092\u8a08\u7b97\u3059\u308b\u5f0f\u306f<\/strong>\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/espoir-mathematiques-valeur-attendue.png\" alt=\"\u6570\u5b66\u7684\u306a\u671f\u5f85\u5024\u307e\u305f\u306f\u671f\u5f85\u5024\" class=\"wp-image-1752\" width=\"279\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u4ee5\u4e0b\u306e\u8a08\u7b97\u6a5f\u3092\u4f7f\u7528\u3057\u3066\u3001\u4efb\u610f\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u671f\u5f85\u5024\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/u><\/p>\n<p>\u4e0a\u8a18\u306e\u5f0f\u306f\u3001\u78ba\u7387\u5909\u6570\u304c\u96e2\u6563\u7684\u3067\u3042\u308b\u5834\u5408\u306b\u306e\u307f\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044 (\u307b\u3068\u3093\u3069\u306e\u5834\u5408)\u3002\u305f\u3060\u3057\u3001\u5909\u6570\u304c\u9023\u7d9a\u5024\u306e\u5834\u5408\u3001\u6570\u5b66\u7684\u671f\u5f85\u5024\u3092\u53d6\u5f97\u3059\u308b\u306b\u306f\u6b21\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c0ecbcb5a0ab0deb8d097268ac2911f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E(X)=\\int_\\mathbb{R} x\\cdot f_x(x) dx \" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"174\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u91d1<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f27dd617611a2ded87c3e79c1ee76fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f_x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u9023\u7d9a\u5909\u6570\u306e\u5bc6\u5ea6\u95a2\u6570\u3067\u3059<\/p>\n<h2 class=\"wp-block-heading\" id=\"ejemplo-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-esperanza-matematica\"><\/span>\u6570\u5b66\u7684\u671f\u5f85\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024) \u306e\u5b9a\u7fa9\u3092\u8003\u616e\u3057\u3066\u3001\u8a08\u7b97\u304c\u3069\u306e\u3088\u3046\u306b\u884c\u308f\u308c\u308b\u304b\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3001\u4ee5\u4e0b\u306b\u5177\u4f53\u7684\u306a\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u4eba\u306f\u3001\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u3066\u51fa\u305f\u6570\u5b57\u306b\u57fa\u3065\u3044\u3066\u304a\u91d1\u306e\u52dd\u3061\u8ca0\u3051\u304c\u6c7a\u307e\u308b\u30b2\u30fc\u30e0\u306b\u53c2\u52a0\u3057\u307e\u3059\u3002 1 \u304c\u51fa\u305f\u5834\u5408\u306f $800 \u3092\u7372\u5f97\u3057\u30012 \u307e\u305f\u306f 3 \u304c\u51fa\u305f\u5834\u5408\u306f $500 \u3092\u5931\u3044\u30014\u30015\u3001\u307e\u305f\u306f 6 \u304c\u51fa\u305f\u5834\u5408\u306f $100 \u3092\u7372\u5f97\u3057\u307e\u3059\u3002\u53c2\u52a0\u8cbb\u306f50\u30c9\u30eb\u3067\u3059\u3002\u3053\u306e\u78ba\u7387\u30b2\u30fc\u30e0\u306b\u53c2\u52a0\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u304b?<\/li>\n<\/ul>\n<p>\u6700\u521d\u306b\u884c\u3046\u3053\u3068\u306f\u3001\u5404\u30a4\u30d9\u30f3\u30c8\u306e\u78ba\u7387\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u30b5\u30a4\u30b3\u30ed\u306b\u306f 6 \u3064\u306e\u9762\u304c\u3042\u308b\u305f\u3081\u3001\u4efb\u610f\u306e\u6570\u5b57\u304c\u51fa\u308b\u78ba\u7387\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b6f7689a151fef994183ad359ae578b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{obtener un n\\'umero})=\\cfrac{1}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5404\u30a4\u30d9\u30f3\u30c8\u306e\u767a\u751f\u78ba\u7387\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3ad9bd3479cfff0fd8a669549b972ecb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{ganar }\\$800)=\\cfrac{1}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cc814922859e0fd0be7476101a6decc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{perder }\\$500)=2\\cdot \\cfrac{1}{6}=\\cfrac{2}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b2a717f65fcc37f0ec7e338271bef523_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p(\\text{ganar }\\$100)=3\\cdot \\cfrac{1}{6}=\\cfrac{3}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"199\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5404\u30a4\u30d9\u30f3\u30c8\u306e\u767a\u751f\u78ba\u7387\u304c\u308f\u304b\u3063\u305f\u306e\u3067\u3001\u671f\u5f85\u5024\u306e\u6570\u5f0f\u3092\u9069\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2634d90a3d741a7681987d3e7f45ebd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E(X)=\\sum_{i=1}^nx_i\\cdot p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"139\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u3001\u6570\u5b66\u7684\u306a\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3a7532f7bc4f9a6fc9c367fe2e28d0bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X)=800\\cdot\\cfrac{1}{6}-500\\cdot \\cfrac{2}{6}+100\\cdot\\cfrac{3}{6}=\\$16,67\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"338\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u671f\u5f85\u5024\u306f\u3053\u306e\u30b2\u30fc\u30e0\u306b\u53c2\u52a0\u3059\u308b\u4fa1\u683c\u3088\u308a\u3082\u4f4e\u3044\u305f\u3081\u3001\u9577\u671f\u7684\u306b\u306f\u304a\u91d1\u3092\u5931\u3046\u3053\u3068\u306b\u306a\u308b\u305f\u3081\u3001\u30d7\u30ec\u30a4\u3057\u306a\u3044\u65b9\u304c\u826f\u3044\u3067\u3057\u3087\u3046\u3002 1\u306b\u306a\u3063\u305f\u3068\u304d\u3060\u3051\u53c2\u52a0\u3059\u308c\u3070\u5927\u304d\u306a\u5229\u76ca\u304c\u5f97\u3089\u308c\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u9577\u671f\u7684\u306b\u306f\u640d\u5931\u3092\u88ab\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u3067\u3059\u3002<\/p>\n<p>\u6570\u5b66\u7684\u671f\u5f85\u5024\u306e\u7d50\u679c\u306f\u3001\u4e0d\u53ef\u80fd\u306a\u5024\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u305f\u3068\u3048\u3070\u3001\u3053\u306e\u5834\u5408\u306f 16.67 \u30c9\u30eb\u304c\u5f97\u3089\u308c\u307e\u305b\u3093\u3002 <\/p>\n<h2 class=\"wp-block-heading\" id=\"calculadora-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-esperanza-matematica\"><\/span>\u671f\u5f85\u5024\u8a08\u7b97\u6a5f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u9023\u306e\u7d71\u8a08\u30c7\u30fc\u30bf\u3092\u6b21\u306e\u8a08\u7b97\u6a5f\u306b\u5165\u529b\u3057\u3066\u3001\u671f\u5f85\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u6700\u521d\u306e\u30dc\u30c3\u30af\u30b9\u306b\u5404\u30a4\u30d9\u30f3\u30c8\u306e\u5024\u3092\u5165\u529b\u3057\u30012 \u756a\u76ee\u306e\u30dc\u30c3\u30af\u30b9\u306b\u305d\u306e\u767a\u751f\u78ba\u7387\u3092\u540c\u3058\u9806\u5e8f\u3067\u5165\u529b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u30c7\u30fc\u30bf\u306f\u30b9\u30da\u30fc\u30b9\u3067\u533a\u5207\u3089\u308c\u3001\u5c0f\u6570\u70b9\u3068\u3057\u3066\u30d4\u30ea\u30aa\u30c9\u3092\u4f7f\u7528\u3057\u3066\u5165\u529b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<form action=\"\" method=\"post\">\n<ul>\n<li>\u5404\u30a4\u30d9\u30f3\u30c8\u306e\u5024: <\/li>\n<\/ul>\n<p><textarea name=\"datosX\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"3 4 1 7 5 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los valores de los sucesos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<ul style=\"margin-top:25px\">\n<li>\u5404\u30a4\u30d9\u30f3\u30c8\u306e\u78ba\u7387: <\/li>\n<\/ul>\n<p><textarea name=\"datosP\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"0.1 0.25 0.4 0.05 0.15 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce las probabilidades aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"\u6570\u5b66\u7684\u671f\u5f85\u5024\u3092\u8a08\u7b97\u3059\u308b\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\" id=\"propiedades-de-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-esperanza-matematica\"><\/span>\u6570\u5b66\u7684\u671f\u5f85\u5024\u306e\u6027\u8cea<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6570\u5b66\u7684\u671f\u5f85\u5024\u306e\u7279\u6027\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u5b9a\u6570\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024\u306f\u305d\u308c\u81ea\u4f53\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-564923a9300f678924c2bf5d02fb5821_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(k)=k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u78ba\u7387\u5909\u6570\u306b\u30b9\u30ab\u30e9\u30fc\u3092\u4e57\u7b97\u3057\u305f\u671f\u5f85\u5024\u306f\u3001\u3053\u306e\u5909\u6570\u306b\u3053\u306e\u30b9\u30ab\u30e9\u30fc\u3092\u4e57\u7b97\u3057\u305f\u671f\u5f85\u5024\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-506787cf97f31936eef0579d1471a5bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(k\\cdot X)=k\\cdot E(X)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> 2 \u3064\u306e\u5909\u6570\u306e\u5408\u8a08\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024\u306f\u3001\u5404\u5909\u6570\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024\u306e\u5408\u8a08\u3068\u7b49\u4fa1\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3cfd9f255e02675ec64ec472d0c997c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X+Y)=E(X)+E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4e00\u822c\u306b\u30012 \u3064\u306e\u5909\u6570\u3092\u4e57\u7b97\u3059\u308b\u3068\u3001\u7570\u306a\u308b\u6570\u5b66\u7684\u671f\u5f85\u5024\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002\u7d50\u679c\u304c\u540c\u3058\u306b\u306a\u308b\u306e\u306f\u3001\u5909\u6570\u304c\u72ec\u7acb\u3057\u3066\u3044\u308b\u5834\u5408\u306e\u307f\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-116cfab17848d8aa4a3833600bd3215a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(X\\cdot Y)\\neq E(X)\\cdot E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5909\u6570\u306e\u3059\u3079\u3066\u306e\u5024\u304c\u30bc\u30ed\u4ee5\u4e0a\u306e\u5834\u5408\u3001\u305d\u306e\u5909\u6570\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024\u3082\u6b63\u307e\u305f\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4830aa6f68f621f7bac3ffa0b2d8d2db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\geq 0 \\ \\longrightarrow \\ E(X)\\geq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"175\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> 1 \u3064\u306e\u5909\u6570\u306e\u3059\u3079\u3066\u306e\u5024\u304c\u5225\u306e\u5909\u6570\u306e\u3059\u3079\u3066\u306e\u5024\u3088\u308a\u3082\u5c0f\u3055\u3044\u5834\u5408\u30012 \u3064\u306e\u5909\u6570\u306e\u671f\u5f85\u5024\u306f\u540c\u3058\u95a2\u4fc2\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f236222136aa7e5cab6ff999cfbecb9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\leq Y \\ \\longrightarrow \\ E(X)\\leq E(Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"213\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5909\u6570\u304c 2 \u3064\u306e\u5024\u306b\u3088\u3063\u3066\u5236\u9650\u3055\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u306e\u6570\u5b66\u7684\u671f\u5f85\u3082\u8ad6\u7406\u7684\u306b\u5236\u9650\u3055\u308c\u307e\u3059\u3002 <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f1241572e77188af4dbd932f7415c0dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\n\n<ul>\n<li> Si une variable est la combinaison lin\u00e9aire d&#8217;une autre variable, ses attentes math\u00e9matiques satisfont \u00e0 la m\u00eame relation alg\u00e9brique : <\/li>\n<\/ul>\n<p>[latex]Y=a+bX \\ \\longrightarrow \\ E(Y)=a+b\\cdot E(X)&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;41&#8243; width=&#8221;1116&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" id=\"para-que-sirve-la-esperanza-matematica\"><span class=\"ez-toc-section\" id=\"%c2%bfpara-que-sirve-la-esperanza-matematica\"><\/span>\u6570\u5b66\u7684\u671f\u5f85\u5024\u306f\u4f55\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u306e\u6700\u5f8c\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u6570\u5b66\u7684\u5e0c\u671b\u306e\u610f\u5473\u3092\u3055\u3089\u306b\u6df1\u304f\u6398\u308a\u4e0b\u3052\u3066\u3044\u304d\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u3001\u3053\u306e\u7d71\u8a08\u7684\u5c3a\u5ea6\u304c\u4f55\u306b\u4f7f\u7528\u3055\u308c\u308b\u304b\u3092\u898b\u3066\u3001\u6982\u5ff5\u3092\u3088\u308a\u3088\u304f\u7406\u89e3\u3057\u307e\u3059\u3002<\/p>\n<p>\u6570\u5b66\u7684\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024) \u306f\u3001\u78ba\u7387\u7a7a\u9593\u3067\u9577\u671f\u7684\u306b\u5f97\u3089\u308c\u308b\u3001\u307e\u305f\u306f\u5931\u308f\u308c\u308b\u3068\u4e88\u60f3\u3055\u308c\u308b\u91cf\u306e\u5024\u3092\u6301\u3064\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u6570\u5b66\u7684\u671f\u5f85\u5024\u306f\u9577\u671f\u7684\u306b\u5f97\u3089\u308c\u308b\u30ea\u30bf\u30fc\u30f3\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<p>\u4f01\u696d\u306e\u682a\u5f0f\u3092\u8cfc\u5165\u3059\u308b\u306a\u3069\u3001\u6295\u8cc7\u3092\u691c\u8a0e\u3059\u308b\u5834\u5408\u3001\u8003\u616e\u3059\u3079\u304d\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e 1 \u3064\u306f\u6570\u5b66\u7684\u671f\u5f85\u5024\u3067\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u3053\u306e\u6295\u8cc7\u3092\u6570\u56de\u884c\u3063\u305f\u5834\u5408\u306b\u5f97\u3089\u308c\u308b\u7d4c\u6e08\u7684\u5229\u76ca\u306f\u3001\u6570\u5b66\u7684\u671f\u5f85\u5024\u306b\u306a\u308b\u304b\u3089\u3067\u3059\u3002\u3053\u308c\u306f\u5f97\u3089\u308c\u308b\u5229\u76ca\u306e\u5e73\u5747\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u540c\u69d8\u306b\u3001\u6570\u5b66\u7684\u671f\u5f85\u306f\u8a08\u91cf\u7d4c\u6e08\u5b66\u3001\u91cf\u5b50\u7269\u7406\u5b66\u3001\u8cbf\u6613\u3001\u3055\u3089\u306b\u306f\u751f\u7269\u5b66\u306a\u3069\u306e\u4ed6\u306e\u5206\u91ce\u3067\u3082\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024 (\u307e\u305f\u306f\u671f\u5f85\u5024) \u3068\u306f\u4f55\u304b\u3001\u304a\u3088\u3073\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u6570\u5b66\u7684\u5e0c\u671b\u306e\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\u304c\u898b\u3064\u304b\u308b\u3067\u3057\u3087\u3046\u3002\u3055\u3089\u306b\u3001\u30aa\u30f3\u30e9\u30a4\u30f3\u8a08\u7b97\u6a5f\u3092\u4f7f\u7528\u3057\u3066\u3001\u4efb\u610f\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u671f\u5f85\u5024\u3092\u898b\u3064\u3051 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[],"class_list":["post-79","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 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